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Lagrange identity for polynomials and $ \delta $-codes of lengths $ 7t$ and $ 13t$


Author: C. H. Yang
Journal: Proc. Amer. Math. Soc. 88 (1983), 746-750
MSC: Primary 05B20; Secondary 05A19, 94B99
DOI: https://doi.org/10.1090/S0002-9939-1983-0702312-0
MathSciNet review: 702312
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Abstract: It is known that application of the Lagrange identity for polynomials (see [1]) is the key to composing four-symbol $ \delta $-codes of length $ (2s + 1)t$ for $ s = {2^a}{10^b}{26^c}$ and odd $ t \leqslant 59$ or $ t = {2^d}{10^e}{26^f} + 1$, where $ a$, $ b$, $ c$, $ d$, $ e$ and $ f$ are nonnegative integers. Applications of the Lagrange identity also lead to constructions of four-symbol $ \delta $-codes of length $ u$ for $ u = 7t$ or $ 13t$. Consequently, new families of Hadamard matrices of orders $ 4uw$ and $ 20uw$ can be constructed, where $ w$ is the order of Williamson matrices. Related topics on zero correlation codes are also discussed.


References [Enhancements On Off] (What's this?)

  • [1] C. H. Yang, A composition theorem for $ \delta $-codes (to appear).
  • [2] -, Hadamard matrices and $ \delta $-codes of length $ 3n$, Proc. Amer. Math. Soc. 85 (1982), 480-482. MR 656128 (84i:05033)
  • [3] -, Hadamard matrices, finite sequences, and polynomials defined on the unit circle, Math. Comp. 33 (1979), 688-693. MR 525685 (80i:05024)
  • [4] R. J. Turyn, Hadamard matrices, Baumert-Hall units, four symbol sequences, pulse compression, and surface wave encodings, J. Combin. Theory Ser. A 16 (1974), 313-333. MR 0345847 (49:10577)
  • [5] -, Computation of certain Hadamard matrices, Notices Amer. Math. Soc. 20 (1973), A-l.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0702312-0
Article copyright: © Copyright 1983 American Mathematical Society

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